Absolute Eigenvalues-Based Covariance Matrix Estimation for a Sparse Array

TL;DR

This paper introduces a robust covariance matrix estimation method for sparse arrays that effectively utilizes both positive and negative eigenvalues, improving accuracy in signal processing applications.

Contribution

The paper proposes a novel covariance matrix estimation technique for augmentable sparse arrays that addresses the issue of negative eigenvalues, enhancing robustness and applicability.

Findings

The proposed method improves signal direction estimation accuracy.

It effectively handles cases with negative noise eigenvalues.

The approach is compatible with subspace algorithms and adaptive beamformers.

Abstract

The ensemble covariance matrix of a wide sense stationary signal spatially sampled by a full linear array is positive semi-definite and Toeplitz. However, the direct augmented covariance matrix of an augmentable sparse array is Toeplitz but not positive semi-definite, resulting in negative eigenvalues that pose inherent challenges in its applications, including model order estimation and source localization. The positive eigenvalues-based covariance matrix for augmentable sparse arrays is robust but the matrix is unobtainable when all noise eigenvalues of the direct augmented matrix are negative, which is a possible case. To address this problem, we propose a robust covariance matrix for augmentable sparse arrays that leverages both positive and negative noise eigenvalues. The proposed covariance matrix estimate can be used in conjunction with subspace based algorithms and adaptive beamformers to yield accurate signal direction estimates.